Simplify the following expression: $ p = \dfrac{-3}{8x - 7} - \dfrac{-6}{7} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-3}{8x - 7} \times \dfrac{7}{7} = \dfrac{-21}{56x - 49} $ Multiply the second expression by $\dfrac{8x - 7}{8x - 7}$ $ \dfrac{-6}{7} \times \dfrac{8x - 7}{8x - 7} = \dfrac{-48x + 42}{56x - 49} $ Therefore $ p = \dfrac{-21}{56x - 49} - \dfrac{-48x + 42}{56x - 49} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-21 - (-48x + 42) }{56x - 49} $ Distribute the negative sign: $p = \dfrac{-21 + 48x - 42}{56x - 49}$ $p = \dfrac{48x - 63}{56x - 49}$